A certain resonant spring system with a periodic forcing function is modeled by $x^{\text{'}\text{'}}(t)+25x(t)=8sin(5t)$ with initial conditions $x(0)=0$ and $x^{\text{'}}(0)=0.$

a$.$ Reduce the problem into a set of first order differential equations in the canonical form.

$(4$ marks$)$

b$.$ Write a short Matlab$/$Octave code to find $x(t)$ over the interval $t=[0,1]$ using ode$45$ along with a user$-$defined function.

$(14$ marks$)$

c$.$ From your solution in b$.,$ state the value for $x(1).$

$(2$ marks$)$